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- Title
Descente fidèlement plate pour les n-champs d’Artin.
- Authors
Toën, Bertrand
- Abstract
We prove two flat descent results in the setting of Artin n-stacks. First of all, a stack for the etale topology which is an Artin n-stack (in the sense of Simpson and Toën–Vezzosi) is also a stack for the flat (fppf) topology. Moreover, an n-stack, for the fppf topology, which admits a flat (fppf) n-atlas is an Artin n-stack (i.e. possesses a smooth n-atlas). We deduce from these two results a comparison between etale and fppf cohomologies (with coefficients in non-smooth group schemes and also non-abelian). This work is written in the setting of the derived stacks of Toën and Vezzosi, and all of these results are therefore also valid for derived Artin n-stacks.
- Subjects
ARTIN algebras; HOMOLOGY theory; ALGEBRAIC stacks; TOPOLOGY; GROUP schemes (Mathematics); ABELIAN groups; MATHEMATICAL proofs
- Publication
Compositio Mathematica, 2011, Vol 147, Issue 5, p1382
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X10005245